On Sampling Continuous-Time AWGN Channels
Abstract
For a continuous-time additive white Gaussian noise (AWGN) channel with possible feedback, it has been shown that as sampling gets infinitesimally fine, the mutual information of the associative discrete-time channels converges to that of the original continuous-time channel. We give in this paper more quantitative strengthenings of this result, which, among other implications, characterize how over-sampling approaches the true mutual information of a continuous-time Gaussian channel with bandwidth limit. The assumptions in our results are relatively mild. In particular, for the non-feedback case, compared to the Shannon-Nyquist sampling theorem, a widely used tool to connect continuous-time Gaussian channels to their discrete-time counterparts that requires the band-limitedness of the channel input, our results only require some integrability conditions on the power spectral density function of the input.
Cite
@article{arxiv.2002.02716,
title = {On Sampling Continuous-Time AWGN Channels},
author = {Guangyue Han and Shlomo Shamai},
journal= {arXiv preprint arXiv:2002.02716},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:1810.08089